Averages andK-Functionals Related to the Laplacian Original Research Article

ForRdorTd, averages on balls and spheres are shown to satisfy an equivalence relation withK-functionals that are generated by the Laplacian. The converse result is given in terms of strong converse inequality of type A and type D for the averages on the Ball and on the sphere, respectively. Combinations of averages on concentric balls and spheres yield strong converse results of type B for higher levels of smoothness.